Answer
It was not possible for Jesus to have sinned even in his capacity as a human. This is partly because of the perfect union of his two natures (human and divine) in the one person whom we know as Jesus Christ, Second Person of the Trinity. It is also partly because of the nature of his human nature.
When we talk of such mysterious doctrines as the hypostatic union of Christ's two natures, it can become very bewildering. Jesus had one person and two natures, and each nature retains its own attributes. That means that anything native to God's nature is native to Jesus' divine nature. And anything native to man's nature is native to Jesus' human nature. However, the ability to sin is not native to human nature. We know this simply by looking at what the Bible teaches about our final state of glorification. In that state, we will still be fully human, but we will no longer be able to sin. Thus, the ability to sin is not an essential element of human nature.
The Bible does not explicitly answer for us the question as to why Adam and Eve had the ability to sin. However, covenant theology reasonably demonstrates that it was in order to test them to see how they would react, as well as in order to bring about the events that God had ordained which were contingent upon human sin. Part of the reason that the rest of humanity has the ability to sin mirrors this first reason, and part of it is the result of the curse that befell mankind as a result of Adam's sin. In any event, the ability to sin is only a temporary human condition, not an innate aspect of human nature.
Because Jesus had a perfect human nature, he had no innate ability to sin. Further, being miraculously free from the consequences of Adam's sin, he was not afflicted with the curse of the ability to sin. Moreover, it was not necessary that Jesus have the ability to sin in order to bring about the events which God had ordained to be contingent upon Jesus' actions.
Also, because Jesus' perfect human nature was united to his divine nature in the one person Jesus Christ, Second Person of the Trinity, and because God cannot sin, the person Jesus was incapable of sin. That is, the nature cannot operate independently of the person. For Jesus to sin in his human nature would require the active cooperation of his person. Persons sin, not natures.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.